Am I obligated to maintain ties with my maternal half-brother, given that my mother refuses due to his past mistreatment of her, and he does not lead a righteous life?

The questioner must maintain ties of kinship and not obey his mother in severing them, because obedience is only in what is good, and severing ties of kinship is not among what is good. He must maintain ties with his brother, call him to Allah, and rectify his situation without his mother's knowledge, so as not to anger her.